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This section calculates an expected value for a 4 point arc in the NBA.

To calculate where a 4 point line should be on an NBA court, I needed to find the expected value for a 4 point shot. To do this, I decided to use data from the past 10 years for the Minnesota Timberwolves, because gathering shot data from every single team over many years would likely be too much to handle, especially since taking it over many years would likely result with similar findings regardless of what team is being looked at. I also decided to look at more recent years, because that makes our findings more relevant to today.

To start, I calculated the expected value for 2 and 3 point shots, which looks like this: Expected shot value (n) = (total n pointers made * n) / total n pointer attempts. From this, I got ~1.02 for 2 pointers and ~1.06 for 3 pointers. Because these values are 0.04 apart, I decided that the optimal place for a 4 point line would be where the corresponding shots line up with an expected value around 1.10, which would be an additional 0.04 above the 3 point expected value. I then calculated the expected values for 4 point shots at various distances, finding that the expected value at 27 or more feet from the hoop is ~1.16 and at 28 or more feet it is ~0.95. From this, I can conclude that the ideal distance for a 4 point arc, given that it is just a simply-shaped arc, would be at about 27.7 feet away from the hoop (which gets the expected value to be ~1.10).

One consequence of adding a 4 point line to the NBA could be that the entire nature of the game could be changed. If players now have more incentive for taking longer shots, there would most likely be less shots taken at the 3 point and especially the 2 point range. In my eyes, this would make basketball a much more offense-dominated sport, because it would make the court more spread out. Players would not go for 2 point shots as often, and the potential for rebounds and defense in that area would lessen.